Theorems · Theorem · general topology
IsUltrametricDist.nnnorm_nsmul_le
∀ {S : Type u_1} [inst : SeminormedAddGroup S] [IsUltrametricDist S] (x : S) (n : ℕ), ‖n • x‖₊ ≤ ‖x‖₊- Defined in
- Mathlib.Analysis.Normed.Group.Ultra
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 116 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- NNRealstatement · cited by 4,310
- NNNorm.nnnormstatement and proof · cited by 952
- zero_leproof · cited by 382
- SeminormedAddGroupstatement and proof · cited by 331
- IsUltrametricDiststatement and proof · cited by 177
- sup_of_le_rightproof · cited by 143
- zero_nsmulproof · cited by 137
- one_nsmulproof · cited by 63
- add_nsmulproof · cited by 44
- nnnorm_zeroproof · cited by 40
- IsUltrametricDist.nnnorm_add_le_maxproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- IsUltrametricDist.nnnorm_zsmul_leproof · cited by 1
- IsUltrametricDist.norm_nsmul_leproof · cited by 0